ELEC6214 Advanced Wireless Communications Networks and Systems
S Chen
Revision of Previous Six Lectures
• Previous six lectures have concentrated on Modem,
under ideal AWGN or flat fading channel condition
• Important issues discussed need to be revised, and
they are summarised in Revisions before each lecture
multiplexing
b(k)
bits to
symbols
x(k)
pulse
generator
symbols
to bits
^x(k)
sampler/
decision
Wireless
Channel
carrier
Tx filter
GT (f)
x(t)
s(t)
modulat.
carrier
recovery
clock
recovery
^b(k)
MODEM
CODEC
clock
pulse
multiple access
Rx filter
GR (f)
^x(t)
channel
GC(f)
^
s(t)
demodul.
+
AWGN
n(t)
• We have not yet discussed carrier recovery for QAM and clock recovery for multilevel signalling ⇒
this lecture, as well as some other issues
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ELEC6214 Advanced Wireless Communications Networks and Systems
S Chen
Carrier Recovery for QAM
• Recall that carrier recovery operates in RF receive signal, which in QAM case
contains in-phase and quadrature components
– Time-2 carrier recovery does not work for quadrature modulation
– This is because I and Q branches have equal average signal power, square RF
signal r(t) leads to low RF signal level
• More specifically, simply consider the squared r(t):
r 2(t) = (aR(t) cos(ωct + φ) + aI (t) sin(ωct + φ))2
1 2
1 2
=
a (t)(1 + cos(2ωct + 2φ)) + aI (t)(1 − cos(2ωct + 2φ))
2 R
2
+aR(t)aI (t) sin(2ωct + 2φ)
– a2R(t) cos(2ωct + 2φ) and −a2I (t) cos(2ωct + 2φ) almost cancel out on average
– aR(t)aI (t) has very low correlation, thus last term is almost zero on average
• Therefore, the baseband signals a2R (t) and a2I (t) dominate, and the carrier could
not be recovered from r 2(t)
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ELEC6214 Advanced Wireless Communications Networks and Systems
S Chen
Time-4 Carrier Recovery for QAM
• Raising to 4th power works: as this generates significant component cos(4(ωct+θ))
at 4ωc, and in theory dividing this component by 4 gets carrier cos(ωct + θ)
• Time-4 carrier recovery
PLL
r(t)
time 4
e(t)
c(t) VCO
LPF
fc
fc
cos(2π fc t + θ )
time 4
– As VCO operates at fc not 4fc, feedback must raised to 4th power
– PLL does not operate at 4fc: high frequency electronics more expensive and
harder to build
• After carrier recovery, clock recovery operates in I or Q baseband signals
– For 4QAM, I or Q is 2-ary (BPSK). Thus, time-2, early-late and zero-crossing
clock recovery schemes all work for 4QAM
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ELEC6214 Advanced Wireless Communications Networks and Systems
S Chen
Clock Recovery for High-Order QAM
• Time-2 clock recovery: for 16QAM or higher, it does not work satisfactorily
– I or Q are multilevel (e.g. I or Q of 16QAM: -3,-1,+1+3), and the symbol-rate
component is less clear in the squared signal
• Early-late clock recovery: for 16QAM or higher, it also works less satisfactorily
– Squared waveform peaks do not always occur every sampling period, and worst
still half of the peaks have wrong polarity
• Zero-crossing clock recovery: for 16QAM or higher, it also works less satisfactorily
– Only some of zero crossings occur at middle of sampling period, and logic circuit
is required to adjust sampling instances correctly
• Synchroniser clock recovery: works well for QAM but requires extra bandwidth
– Synchroniser clock recovery is usually applied in initial link synchronisation
– During data communication phase, alternative synchronisation required
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ELEC6214 Advanced Wireless Communications Networks and Systems
S Chen
Why E-L not Work for High-Order QAM
E-L Scheme for 16QAM example:
• Left graph: the middle symbol represents
the symbol period in which peak detection
is attempted
• Right graph: the sampling instance is early
If sampling instance is early
(a) E − L < 0 → early, correct decision
(b) E − L > 0 → late, wrong decision
(c) E − L < 0 → early, correct decision
If sampling instance is late
(a) E − L > 0 → late, correct decision
(b) E − L < 0 → early, wrong decision
(c) E − L < 0 → early, wrong decision
Thus E −L Scheme has 50% wrong polarity
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ELEC6214 Advanced Wireless Communications Networks and Systems
S Chen
Modified Early-Late Clock Recovery
• As previous slide shows, there
are three cases of squared
waveform: (a) positive peak, (b)
negative peak, (c) no peak
• To make scheme work, key is:
– Decision rules for updating
sampling instance using
difference between E and L
should be different for cases
(a) and (b)
– In case of no peak, it is
better no updating at all, as
50% of times will be wrong
• Modified E-L scheme adopts
oversampling in one symbol
period, say, n samples {Ri }ni=1 ,
instead of just two samples E
and L
• It detects which of (a), (b) and (c) cases occurs and take corresponding action
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ELEC6214 Advanced Wireless Communications Networks and Systems
S Chen
Modified E-L Clock Recovery (continue)
• For convenience, we will use Rp to denote either the maximum or the minimum of {Ri }ni=1
⋄ If Max Rp is at either
end, no positive peak
⋄ If Min Rp is at either
end, no negative peak
Rp
Rp
Rp
Rp
negative peak only
Rp
Rp
positive peak only
no peak at all
⋄ If Max Rp is at one end
and Min Rp at the other end, no peak at all and do nothing (PLL free run)
Rp
generic
which dominant?
Rp
• How to find positive and/or negative peaks
gradients for confirming positive peak
+
G+
+2 = Rp − Rp+2 , G+3 = Rp − Rp+3
+
G+
−2 = Rp − Rp−2 , G−3 = Rp − Rp−3
G+
+23 = Rp+2 − Rp+3
+
G−23 = Rp−2 − Rp−3
gradients for confirming negative peak
−
G−
+2 = Rp+2 − Rp , G+3 = Rp+3 − Rp
−
G−
−2 = Rp−2 − Rp , G−3 = Rp−3 − Rp
G−
+23 = Rp+3 − Rp+2
−
G−23 = Rp−3 − Rp−2
– Rp±1 are not used: due to the nature of pulse shaping, they are similar to Rp
• If only a positive or negative peak, it is dominant; if both peaks exist, which is dominant is
determined by calculating Pscore and Nscore and comparing them
• The difference between the current sampling time and the dominant peak is used to drive PLL
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ELEC6214 Advanced Wireless Communications Networks and Systems
S Chen
Odd-Bit QAM
• Square QAM constellation requires even number of bits per symbol
– Throughput requirement may need scheme with odd number of bits per symbol
• To transmit odd number of bits per symbol,
“rectangular” scheme could be used
– An example of 5-bit rectangular QAM may
looks like
– Bad as I and Q signals would be treated
differently
• “Symmetric” constellation is better
– 5-bit QAM example:
– Inphase and quadrature components are symmetric
– Constellation points most affected by nonlinear
distortion of RF amplifier and/or channel are omitted
• This principle widely adopted in very high-order QAM,
such as microwave trunk link
I
Q
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ELEC6214 Advanced Wireless Communications Networks and Systems
S Chen
Star QAM
• In Lecture 7, we learn square QAM is optimal for AWGN, but star QAM or
product-APSK is better for fading channels
– Recall slide 95, square 16QAM has 20% higher minimum distance at same average
energy than star 16QAM, but latter has larger minimum phase separation
Q
3
• Star 16QAM example
– Four bits b1b2b3b4 per symbol for star
16QAM, as for square 16QAM
– I and Q amplitudes for star 16QAM:
0, ±0.707, ±1, ±2.12, ±3 (d dropped
for convenience)
– Compare this with ±3, ±1 for square
16QAM
• There are unexpected consequences
1
-3
-1
1
3
I
-1
-3
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ELEC6214 Advanced Wireless Communications Networks and Systems
S Chen
Star QAM: Clock Recovery
• Raised cosine pulse shaped I or Q channel: peaks are not always coincide with equispaced sampling
points, see figure (a), which will cause serious problem for clock recovery
– Timing recovery often relies on peaks occurring at equispaced sampling points
• Using nonlinear filtering to make peaks at symbol-spaced, at the cost of small extra bandwidth, the
PSD of this NLF:
«2
„
sin(2πf Ts )
1
S(f ) = Ts
2πf Ts 1 − 4(f Ts )2
• I or Q channel before (a) and after (b) NLF
(a)
(b)
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ELEC6214 Advanced Wireless Communications Networks and Systems
S Chen
Differential Coding for Star 16QAM
• For star 16QAM, we can have coherent detection, which requires expensive carrier recovery
– Star 16QAM has advantage in non-coherent detection with differential coding, particularly for
fading environment
• There are two phasor amplitudes for star 16QAM, and first bit b1 differentially encoded onto QAM
phasor amplitude, i.e. deciding which phasor ring
– b1 = 1: current symbol changes to amplitude ring not used in previous symbol
– b1 = 0: current symbol remains at amplitude ring used in previous symbol
• There are 8 different phases, and remaining three bits b2 b3b4 are differentially Gray encoded onto
phase, i.e. deciding which phase
• An example of this differentially Gray encoded phase
– 000: current symbol transmitted with same phase as previous one
– 001: current symbol transmitted with 45 degree phase shift relative to previous one
– 011: current symbol transmitted with 90 degree phase shift relative to previous one
– 010: current symbol transmitted with 135 degree phase shift relative to previous one
– 110: current symbol transmitted with 180 degree phase shift relative to previous one
– 111: current symbol transmitted with 225 degree phase shift relative to previous one
– 101: current symbol transmitted with 270 degree phase shift relative to previous one
– 100: current symbol transmitted with 315 degree phase shift relative to previous one
• Initial condition, i.e. amplitude and phase of initial symbol s0 is fixed, and known to receiver
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ELEC6214 Advanced Wireless Communications Networks and Systems
S Chen
Differential Decoding for Star 16QAM
• Let two amplitude levels of star 16QAM be A1 and A2; received amplitudes at k
and k − 1 be Zk and Zk−1; received phases at k and k − 1 be θk and θk−1
• Decision rule for first bit b1: If Zk ≥
otherwise b1 = 0
A1 +A2
Zk−1
2
or Zk <
2
A1 +A2 Zk−1
b1 = 1;
Simulated 16QAM in Rayleigh channel
• Decision rule for remaining bits b2b3b4: Let
square
−1
θdem = (θk − θk−1) mod 2π
10
θdem is quantised to nearest 0◦, 45◦, 95◦,
135◦, 180◦, 225◦ or 270◦, 315◦
10
Quantised θdem is used to output b2b3b4
according to Gray encoding rule look up table
• Star 16QAM has better BER (order 2
improvement) than square one in fading
BER
−2
star
−3
10
−4
10
−5
10
star
AWGN
SNR (dB)
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ELEC6214 Advanced Wireless Communications Networks and Systems
S Chen
Summary
• Carrier recovery for QAM: Why time-2 carrier recovery does not work for QAM,
Time-4 carrier recovery for QAM
• Clock recovery methods for binary modulation have problems for 16QAM or higher
except synchroniser
– Why early-late clock recovery does not work satisfactorily for 16QAM or higher
– How modified early-late clock recovery works
• Non-square old-bit QAM constellations
• Non-square star QAM:
– Raised cosine pulse shaped I and Q: peaks are not always at symbol-spaced
points, and this time recovery difficulty can be overcome by nonlinear filtering
– Differential encoding and decoding for star 16QAM, BER performance
comparison with square 16QAM
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